1. **State the problem:** Simplify the expression $$\sqrt{3} - 0.0027 - 2^{-0.5} \times 1.28^{0.5}$$. 2. **Recall the rules and formulas:** - The square root of a number $a$ is written as $\sqrt{a} = a^{0.5}$. - Negative exponents mean reciprocal: $a^{-b} = \frac{1}{a^b}$. - Multiplication and subtraction follow normal arithmetic rules. 3. **Calculate each term:** - $\sqrt{3} = 3^{0.5} \approx 1.732$ - $2^{-0.5} = \frac{1}{2^{0.5}} = \frac{1}{\sqrt{2}} \approx 0.707$ - $1.28^{0.5} = \sqrt{1.28} \approx 1.131$ 4. **Multiply the terms with exponents:** $$2^{-0.5} \times 1.28^{0.5} \approx 0.707 \times 1.131 = 0.800$$ 5. **Substitute back and simplify:** $$\sqrt{3} - 0.0027 - 0.800 \approx 1.732 - 0.0027 - 0.800$$ 6. **Perform the subtraction:** $$1.732 - 0.0027 = 1.7293$$ $$1.7293 - 0.800 = 0.9293$$ **Final answer:** $$\boxed{0.9293}$$